2,707 research outputs found
Exploiting the Temporal Logic Hierarchy and the Non-Confluence Property for Efficient LTL Synthesis
The classic approaches to synthesize a reactive system from a linear temporal
logic (LTL) specification first translate the given LTL formula to an
equivalent omega-automaton and then compute a winning strategy for the
corresponding omega-regular game. To this end, the obtained omega-automata have
to be (pseudo)-determinized where typically a variant of Safra's
determinization procedure is used. In this paper, we show that this
determinization step can be significantly improved for tool implementations by
replacing Safra's determinization by simpler determinization procedures. In
particular, we exploit (1) the temporal logic hierarchy that corresponds to the
well-known automata hierarchy consisting of safety, liveness, Buechi, and
co-Buechi automata as well as their boolean closures, (2) the non-confluence
property of omega-automata that result from certain translations of LTL
formulas, and (3) symbolic implementations of determinization procedures for
the Rabin-Scott and the Miyano-Hayashi breakpoint construction. In particular,
we present convincing experimental results that demonstrate the practical
applicability of our new synthesis procedure
Tree Regular Model Checking for Lattice-Based Automata
Tree Regular Model Checking (TRMC) is the name of a family of techniques for
analyzing infinite-state systems in which states are represented by terms, and
sets of states by Tree Automata (TA). The central problem in TRMC is to decide
whether a set of bad states is reachable. The problem of computing a TA
representing (an over- approximation of) the set of reachable states is
undecidable, but efficient solutions based on completion or iteration of tree
transducers exist. Unfortunately, the TRMC framework is unable to efficiently
capture both the complex structure of a system and of some of its features. As
an example, for JAVA programs, the structure of a term is mainly exploited to
capture the structure of a state of the system. On the counter part, integers
of the java programs have to be encoded with Peano numbers, which means that
any algebraic operation is potentially represented by thousands of applications
of rewriting rules. In this paper, we propose Lattice Tree Automata (LTAs), an
extended version of tree automata whose leaves are equipped with lattices. LTAs
allow us to represent possibly infinite sets of interpreted terms. Such terms
are capable to represent complex domains and related operations in an efficient
manner. We also extend classical Boolean operations to LTAs. Finally, as a
major contribution, we introduce a new completion-based algorithm for computing
the possibly infinite set of reachable interpreted terms in a finite amount of
time.Comment: Technical repor
String rewriting for Double Coset Systems
In this paper we show how string rewriting methods can be applied to give a
new method of computing double cosets. Previous methods for double cosets were
enumerative and thus restricted to finite examples. Our rewriting methods do
not suffer this restriction and we present some examples of infinite double
coset systems which can now easily be solved using our approach. Even when both
enumerative and rewriting techniques are present, our rewriting methods will be
competitive because they i) do not require the preliminary calculation of
cosets; and ii) as with single coset problems, there are many examples for
which rewriting is more effective than enumeration.
Automata provide the means for identifying expressions for normal forms in
infinite situations and we show how they may be constructed in this setting.
Further, related results on logged string rewriting for monoid presentations
are exploited to show how witnesses for the computations can be provided and
how information about the subgroups and the relations between them can be
extracted. Finally, we discuss how the double coset problem is a special case
of the problem of computing induced actions of categories which demonstrates
that our rewriting methods are applicable to a much wider class of problems
than just the double coset problem.Comment: accepted for publication by the Journal of Symbolic Computatio
Abstract Symbolic Automata: Mixed syntactic/semantic similarity analysis of executables
We introduce a model for mixed syntactic/semantic approximation of programs based on symbolic finite automata (SFA). The edges of SFA are labeled by predicates whose semantics specifies the denotations that are allowed by the edge. We introduce the notion of abstract symbolic finite automaton (ASFA) where approximation is made by abstract interpretation of symbolic finite automata, acting both at syntactic (predicate) and semantic (denotation) level. We investigate in the details how the syntactic and semantic abstractions of SFA relate to each other and contribute to the determination of the recognized language. Then we introduce a family of transformations for simplifying ASFA. We apply this model to prove properties of commonly used tools for similarity analysis of binary executables. Following the structure of their control flow graphs, disassembled binary executables are represented as (concrete) SFA, where states are program points and predicates represent the (possibly infinite) I/O semantics of each basic block in a constraint form. Known tools for binary code analysis are viewed as specific choices of symbolic and semantic abstractions in our framework, making symbolic finite automata and their abstract interpretations a unifying model for comparing and reasoning about soundness and completeness of analyses of low-level code
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